1. Piezoresistive Sensors - Principles, Materials, Fabrication and Applications
Chang Liu
Micro Actuators, Sensors, Systems Group
University of Illinois at Urbana-Champaign
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2. Definition of Piezoresistive Sensing
Also called strain sensors or strain gauges.
A strain gauge is a device used to measure how much a component distorts under loading.
The electrical resistance of a sensing material changes as a result of applied strains.
A strain gauge is a conductor or semiconductor material that can be directly fabricated on the sensor itself or bonded with the sensor.
In macroscopic systems, such as strain sensors in machine tools, aircraft, strain gauges are most likely bonded onto parts.
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3. Stress-Strain Relation
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4. Physical Causes of Piezoresistivity
Change of relative dimensions, as the resistance is related to length and cross-sectional area (local).
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5. Why Electrical Conductivity Change With Stress/Strain?
Change of electrical conductivity and resistivity as a result of crystal lattice deformation.
Strain causes the shape of energy band curves to change, therefore changing the effective mass, m*. Therefore electrical conductivity s changes.
Crystal bandgap structure
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6. Basic Formula for Describing Piezoresistivity
G is called Gauge Factor of a piezoresistor. It determines the amplification factor between strain and resistance change.
Why the big difference between materials?
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7. Applications at Macroscale
Spot-weldable strain gauges are used with strain gauge sensors and a vibrating wire indicator or data logger to monitor strain in steel members. Typical applications include:
Monitoring structural members of buildings and bridges during and after construction.
Determining load changes on ground anchors and other post-tensioned support systems.
Monitoring load in strutting systems for deep excavations.
Measuring strain in tunnel linings and supports.
Monitoring areas of concentrated stress in pipelines.
Monitoring distribution of load in pile tests.
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8. Metal Strain Gauge
For metals, the resistivity is not changed significantly by the stress. The gauge factor is believed to be contributed by the change of dimensions. These may be made from thin wires or metal films that may be directly fabricated on top of micro structures. Typical strain gauge pattern is shown in the following figure. Thin film strain gauges are typically fabricated on top of flexible plastic substrates and glued to surfaces.
etched foil gauges
These strain gauges consist of a conduction path etched onto metal clad plastic film. The strain gauges are designed to be glued, using very special procedures onto the component to be tested. When the component stretches, the strain gauge will also stretch as will the etched conduction path.
An interactive guide can be found at
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9. Strain gauge selection and use
Metal alloys
Constantan, a Nickel-Cu alloy:
Of all modern strain gage alloys, constantan is the oldest, and still the most widely used.
constantan tends to exhibit a continuous drift at temperatures above +150 deg F (+65 deg C);
Nickel-Chrominum alloy
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10. Two Primary Classes of Piezo-resistor Configuration
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11. Semiconductor Strain Gauge
The very first semiconductor strain gauge used a doped silicon strip attached to a membrane of another material.
In semiconductor strain gauges, the piezoresistive effect is very large, leading to much higher G.
P-type silicon has a G up to 200 and n-type has a negative G of down to -140.
Strain gauges can be locally fabricated in bulk silicon through ion implantation or diffusion
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12. Gauge factor of polysilicon with doping
Gauge factor is a function of doping material or doping concentration.
Because grains are randomly oriented, gauge factor is not sensitive to orientation.
N type
Phosphorous doped Si
P type
Boron doped Si
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14. Why Use Semiconductor Strain Gauge
Higher G than metal alloy strain gauges
Easily fabricated with controlled performance specifications using precise ion implantation and diffusion
Easily integratable with silicon, a material used for sensors and signal processing.
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15. Merit of Piezoresistive Sensors Vs Capacitive
Capacitive sensing is perhaps the most dominant position-sensing technique for microfabricated sensors. However, there are a number of limitations imposed on capacitive sensors.
The detection of position is constrained to small vertical movement (parallel plate) and horizontal movement (transverse or lateral comb drives).
The area of overlapped electrodes must be reasonably large (as a rule of thumb, tens of mm2). If the overlap area is small and the vertical displacement is large, capacitive sensors are not suitable.
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16. Single Crystal Silicon Vs. Polycrystal
Single Crystal Silicon: Uniform crystal orientation throughout the entire material.
Method of growth: heat melt (bulk); epitaxy (thin film)
Polycrystal silicon: crystal orientation exist with in individual grains which are separated by grain boundaries.
Methods of growth: low pressure chemical vapor deposition; sputtering (like a metal).
Single crystal
Polycrystal
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17. The piezoresistive coefficients
Ohm’s law in matrix form
The relation between changes of resistivity and the applied stress and strain
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18. Piezoresistivity Components
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19. Example
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20. Methods for Compensating Temperature Effect
Doped silicon strain sensors are also sensitive to temperature. In order to isolate the effect of temperature and strain, it is important to compensate for the temperature effect.
Common technique: Use a reference resistor which is subject to the same temperature but not the strain. The difference of signal between these two sensors give overall effect due to strain.
Second technique: Wheatstone bridge
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21. Temperature in-sensitive!!
Wheatstone Bridge Circuit - Transforming resistance change to voltage change
Common configuration.
Temperature in-sensitive!!
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22. Strain Gauge Made of Single Crystal Silicon - A Pressure Sensor
Process
Etch backside to form diaphragm with controlled thickness.
Silicon is selectively doped in the region where stress is greatest.
Difference of pressure across the diaphragm will cause stress concentration.
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23. Stress Analysis and Sensor Placement
Sensor placement in the highest stress region.
displacement
Stress
Differential eq.
For displacement.
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24. Pressure Sensor Based On Polysilicon
Sensors placed on edges (highest tensile stress) and center (highest compressive stress).
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25. Fabrication Process
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26. Fabrication Process (Continued)
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28. Piezoresistive Accelerometer
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29. Condition for Mechanical Equilibrium
Total force on a given mechanical member is zero.
Total moment on a given mechanical member is zero.
Tensile
Compressive
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33. Relationship between maximum stress and applied force
The stress within the cross-section provide counter moment (torque) to balance the torque created by the applied force.
The magnitude of the torque is force times the length of arm, l.
Therefore M=Fl.
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34. Example 6.2
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36. Good vs. Bad Designs
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37. Because the longitudinal stress is the greatest at that point.
When one tried to bend a cantilever beam, the failure always occurs at the anchored end and the surface of the beam. Why?
Because the longitudinal stress is the greatest at that point.
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38. Comments on Mechanical Failure
Two failure modes
Fracture
if the strain in the material exceed the fracture strain, the material will undergo catastrophic failure due to fracture.
In design, it is important to not only design the mechanical structure accurately but also to leave safety margins.
Fatigue
If repeated cycle of force is applied to a mechanical member, with the induced strain much lower than that of the fracture strain, the member may failure after repeated cycles.
Mechanism: microscopic defects (bubbles, dislocations) amplifies over time and causes stress concentration (re-distribution of stress). The defects are often hidden underneath the surface of the material.
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39. Stress-Strain Curve
Silicon is a strong material, not a tough material.
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40. Case 6.1: Analysis of Accelerometer
Acceleration induced force F, F=ma.
The force induces stress at the fixed end of the cantilever beam.
The stress is detected by chance in resistance.
Assumptions
assume entire resistance is concentrated at the anchor;
for moment of inertia at the end, ignore the thickness of the resistor.
Assume the stress on the resistor is the maximum value.
The proof mass is rigid. It does not bend because of the significant thickness and width.
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41. Analysis of Sensitivity
Under a given a, the force has a magnitude
The moment applied at the fixed end of the beam is
Therefore the maximum strain, which is the strain experienced by the resistor, is
The strain is applied in the longitudinal direction of the resistor. Assuming the gauge factor is G, the change in resistance is
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42. Stress state analysis example
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43. Stress state analysis example
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